Evaluate the integrals in Exercises 33–54.
∫(e^(3x) + 5e...

Question

Evaluate the integrals in Exercises 33–54.

∫(e^(3x) + 5e^(-x)) dx

Accepted Answer

Welcome back everyone. Find the indefinite integral 5e to the power of 2x plus 3e to the power of -5 XDX. For this problem we can begin by applying the properties of integrals, and we're going to split this integral into two parts. And additionally we can factor out each constant. So for the first integral we will have 5 integral of e to the power of 2 x dx. And for the second one we are going to add 3 integral of e to the power of -5 x dx. Now we want to integrate e to the power of a x dx. Let's remember that the integral of e to the power of a x dx is equal to 1 divided by a e to the power of ax plus a constant of integration c. So for e to the power of 2 x dx, our A is 2, and we get 1 divided by 2. E to the power of 2 x plus a constant of integration. Let's call it c1 and for the second one we get integral of e to the power of -5 x dx, which is going to be -1 divided by 5 because now a is -5 e to the power of -5 x plus a constant of integration c2. So now adding each constant for the first integral, we get 5 multiplied by 1/2, which is 5 halves. E to the power of 2 x plus for the second integral we get 3 multiplied by 1/5 which is -3/5. So we're going to subtract 3/5 e to the power of -5 x and now adding C1 and C2 and specifically when they are multiplied by the corresponding constants, we can just combine those into a single constant of integration c. That's how we get our final answer and thank you for watching.

Evaluate the integrals in Exercises 33–54.∫(e^(3x) + 5e^(-x)) dx

Watch next

Evaluate the integrals in Exercises 33–54.
∫(e^(3x) + 5e^(-x)) dx